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**SebEndo** First find the intersection point: (15/17 , -2/7) (let me know if you have trouble finding this.

Next, because it is a reflected light beam we know the relation between angles: the angle of incidence will be equal to the angle of reflection. let the angle of the mirror line with the horizontal be A and the angle of the beam with the horizontal be B. Draw this out and label the angles and you will find that the angle between the tow line (C) is C=B-A i)

Then, if you draw a horizontal line from the point of intersection you can see that the angle of the reflected beam (D) is: D=C-A ii)

use i) and ii) to isolate D: D=B-2A iii)

lastly we know that the angle of a line with the horizontal is the arctan of its slope. therfore we state that D=arctan(m) ,m being the slope of the reflected light beam. Using iii) we get the folowing equation:

=> arctan(m)=arctan(10)-2*arctan(3)

=> m=tan(arctan(10)-2*arctan(3)) = -43/26